A008847 Numbers k such that sum of divisors of k^2 is a square.

1, 9, 20, 180, 1306, 1910, 11754, 17190, 32486, 38423, 47576, 48202, 50920, 51590, 83884, 104855, 132682, 198534, 247863, 292374, 300876, 312374, 313929, 334330, 345807, 376095, 428184, 433818, 458280, 464310, 469623, 498892, 623615, 754956, 768460, 787127, 943695, 985369

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

Comments

These are the square roots of squares in A006532. - M. F. Hasler, Oct 23 2010

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 10.
• I. Kaplansky, The challenges of Fermat, Wallis and Ozanam (and several related challenges): II. Fermat's second challenge, Preprint, 2002.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..400 (first 161 terms from Zak Seidov)

Crossrefs

Cf. A008848, A008849, A008850, A163763.

Cf. A000203, A010052, A000290.

Programs

Haskell

a008847 n = a008847_list !! (n-1)
a008847_list = filter ((== 1) . a010052 . a000203 . a000290) [1..]
-- Reinhard Zumkeller, Mar 27 2013

Maple

with(numtheory): readlib(issqr): for i from 1 to 10^5 do if issqr(sigma(i^2)) then print(i); fi; od;

Mathematica

s = {}; Do[ If[IntegerQ[ Sqrt[ DivisorSigma[1, n^2]]], Print[n]; AppendTo[s, n]], {n, 10^6}]; s (* Jean-François Alcover, May 05 2011 *)
Select[Range[1000000],IntegerQ[Sqrt[DivisorSigma[1,#^2]]]&] (* Harvey P. Dale, Aug 22 2011 *)

PARI

is_A008847(n)=issquare(sigma(n^2)) \\ M. F. Hasler, Oct 23 2010

Formula

A163763(n) = sqrt(sigma(A008847(n)^2)). - M. F. Hasler, Oct 16 2010

a(n) = sqrt(A008848(n)). - Zak Seidov, May 01 2016